document.write( "Question 210725: Lakota bought 6 new compact disks and 2 used compact disks for $127.92. At the same prices, Mackenzie bought 3 new compact disks and 8 used compact disks for $133.89. Find the cost of buying a single used compact disk. \n" ); document.write( "

Algebra.Com's Answer #159240 by algebrapro18(249) $\"\"$ $\"About$

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Well this is a system of 2 equations and 2 unknowns. Let n = the price of new compact disks and let u = the price of used compact disks. Then the first equation would be 6n + 2u = 127.92. The second equation would be 3n+8u = 133.89.
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\n" ); document.write( "\n" ); document.write( "So our system is
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\n" ); document.write( "\n" ); document.write( "6n + 2u = 127.92
\n" ); document.write( "3n+8u = 133.89
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\n" ); document.write( "\n" ); document.write( "Since I don't like working with decimals I would multiply both equations by 100 that way it would get rid of the decimal. Doing so results in the following system:
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\n" ); document.write( "\n" ); document.write( "600n+200u = 12792
\n" ); document.write( "300n+800u = 13389
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\n" ); document.write( "\n" ); document.write( "now we want to know how much one used disk sells for. to do that we multiply the bottom equation by -2 and add it to the top equation.
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\n" ); document.write( "\n" ); document.write( "-2(300n+800u = 13389) => -300n-1600u = -26778
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\n" ); document.write( "\n" ); document.write( "Now we add that to the top equation
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\n" ); document.write( "\n" ); document.write( "600n+200u = 12792
\n" ); document.write( "+(-300n-1600u = -26778)
\n" ); document.write( "----------------------------
\n" ); document.write( "-1400u = -13987
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\n" ); document.write( "\n" ); document.write( "now we solve for u by dividing both sides by -1400 and we see that u = 9.99.
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\n" ); document.write( "\n" ); document.write( "So the price of a used compact disk is $9.99. \n" ); document.write( "

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